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It was a Platonic concept about space as something given and unchangable. It was an indissoluble partnership between geometrical and philosophical ideas about space and time that developed within theory of ideas. Plato had continually in mind the static shapes discovered by Greek mathematics. On the other hand, Greek geometry will never achieved completion as a real system until it adopted Plato's manner of thinking. Its ideal of science was wholly determined by this, and Euclid's "Elements" are the end and the crown of this way of thinking.
All was finished when so-called noneuclidian geometries appiered.
The space is no more an empty room, which could be filled up with any things. Mathematics is, and in fact always will be, a science of pure relations, and in its modern form it is precisely this feature that has become more and more pronounced. So, when figures of any sort are mentioned and their nature is investigated the inquiry is never into their actual existence but into their relations to one another, in which alone mathematics is interested. Indeed in so far as mathematical thought is concerned their existence does not matter.The single elements receive their roles, and hence their significance, only as they fit together into a connected system; thus they are defined through one another. It is clear that for this theiry any given geometry can be from the first nothing but a certain system of order and relations, whose character is determined by principles governing the relationships, and not by the intrinsic nature of the figures entering into it. Thus, every geometry in its general concept and aim is a theory of invariants with respect to a certain group, and the special nature of each depends upon the choice of this group.
The question about unity of space can therefore be posed only in this sense, that it concerns not the substantial but the formal or "ideal" unity. It was Leibniz who first explained that space is pure "form": an order of coexistence, as time is an order of succession. "Space is indeed something, but just as time is; each is a general order of things. Space is the order of coexistence, and time is the order of successive existence. They are veritable things but they are ideal ones like numbers"
Yours, Boris.